app-proto/sketch-outline/Cargo.toml

@@ -9,6 +9,7 @@ default = ["console_error_panic_hook"]
 
 [dependencies]
 itertools = "0.13.0"
+js-sys = "0.3.70"
 nalgebra = "0.33.0"
 sycamore = "0.9.0-beta.3"
 
@@ -20,6 +21,16 @@ console_error_panic_hook = { version = "0.1.7", optional = true }
 
 [dependencies.web-sys]
 version = "0.3.69"
+features = [
+  'HtmlCanvasElement',
+  'Performance',
+  'WebGl2RenderingContext',
+  'WebGlBuffer',
+  'WebGlProgram',
+  'WebGlShader',
+  'WebGlUniformLocation',
+  'WebGlVertexArrayObject'
+]
 
 [dev-dependencies]
 wasm-bindgen-test = "0.3.34"

app-proto/sketch-outline/src/display.rs

@@ -1,10 +1,342 @@
-use sycamore::prelude::*;
+use core::array;
+use nalgebra::{DMatrix, DVector, Rotation3, Vector3};
+use sycamore::{prelude::*, motion::create_raf};
+use web_sys::{
+    console,
+    window,
+    WebGl2RenderingContext,
+    WebGlProgram,
+    WebGlShader,
+    WebGlUniformLocation,
+    wasm_bindgen::{JsCast, JsValue}
+};
+
+fn compile_shader(
+    context: &WebGl2RenderingContext,
+    shader_type: u32,
+    source: &str,
+) -> WebGlShader {
+    let shader = context.create_shader(shader_type).unwrap();
+    context.shader_source(&shader, source);
+    context.compile_shader(&shader);
+    shader
+}
+
+fn get_uniform_array_locations<const N: usize>(
+    context: &WebGl2RenderingContext,
+    program: &WebGlProgram,
+    var_name: &str,
+    member_name_opt: Option<&str>
+) -> [Option<WebGlUniformLocation>; N] {
+    array::from_fn(|n| {
+        let name = match member_name_opt {
+            Some(member_name) => format!("{var_name}[{n}].{member_name}"),
+            None => format!("{var_name}[{n}]")
+        };
+        context.get_uniform_location(&program, name.as_str())
+    })
+}
+
+// load the given data into the vertex input of the given name
+fn bind_vertex_attrib(
+    context: &WebGl2RenderingContext,
+    index: u32,
+    size: i32,
+    data: &[f32]
+) {
+    // create a data buffer and bind it to ARRAY_BUFFER
+    let buffer = context.create_buffer().unwrap();
+    context.bind_buffer(WebGl2RenderingContext::ARRAY_BUFFER, Some(&buffer));
+    
+    // load the given data into the buffer. the function `Float32Array::view`
+    // creates a raw view into our module's `WebAssembly.Memory` buffer.
+    // allocating more memory will change the buffer, invalidating the view.
+    // that means we have to make sure we don't allocate any memory until the
+    // view is dropped
+    unsafe {
+        context.buffer_data_with_array_buffer_view(
+            WebGl2RenderingContext::ARRAY_BUFFER,
+            &js_sys::Float32Array::view(&data),
+            WebGl2RenderingContext::STATIC_DRAW,
+        );
+    }
+    
+    // allow the target attribute to be used
+    context.enable_vertex_attrib_array(index);
+    
+    // take whatever's bound to ARRAY_BUFFER---here, the data buffer created
+    // above---and bind it to the target attribute
+    //
+    //   https://developer.mozilla.org/en-US/docs/Web/API/WebGLRenderingContext/vertexAttribPointer
+    //
+    context.vertex_attrib_pointer_with_i32(
+        index,
+        size,
+        WebGl2RenderingContext::FLOAT,
+        false, // don't normalize
+        0, // zero stride
+        0, // zero offset
+    );
+}
 
 #[component]
 pub fn Display() -> View {
+    // canvas
+    let display = create_node_ref();
+    
+    // navigation
+    let pitch_up = create_signal(0.0);
+    let pitch_down = create_signal(0.0);
+    let yaw_right = create_signal(0.0);
+    let yaw_left = create_signal(0.0);
+    let roll_ccw = create_signal(0.0);
+    let roll_cw = create_signal(0.0);
+    let zoom_in = create_signal(0.0);
+    let zoom_out = create_signal(0.0);
+    
+    // change listener
+    let scene_changed = create_signal(true);
+    
+    /* INSTRUMENTS */
+    const SAMPLE_PERIOD: i32 = 60;
+    let mut last_sample_time = 0.0;
+    let mut frames_since_last_sample = 0;
+    let mean_frame_interval = create_signal(0.0);
+    
+    on_mount(move || {
+        /* SCAFFOLDING */
+        /* create list of construction elements */
+        const SPHERE_MAX: usize = 200;
+        let mut sphere_vec = Vec::<DVector<f64>>::new();
+        let mut color_vec = Vec::<[f32; 3]>::new();
+        
+        // timing
+        let mut last_time = 0.0;
+        
+        // viewpoint
+        const ROT_SPEED: f64 = 0.4; // in radians per second
+        const ZOOM_SPEED: f64 = 0.15; // multiplicative rate per second
+        let mut orientation = DMatrix::<f64>::identity(5, 5);
+        let mut rotation = DMatrix::<f64>::identity(5, 5);
+        let mut location_z: f64 = 5.0;
+        
+        // display parameters
+        const OPACITY: f32 = 0.5; /* SCAFFOLDING */
+        const HIGHLIGHT: f32 = 0.2; /* SCAFFOLDING */
+        const LAYER_THRESHOLD: i32 = 0; /* DEBUG */
+        const DEBUG_MODE: i32 = 0; /* DEBUG */
+        
+        /* INSTRUMENTS */
+        let performance = window().unwrap().performance().unwrap();
+        
+        // get the display canvas
+        let canvas = display.get().unchecked_into::<web_sys::HtmlCanvasElement>();
+        let ctx = canvas
+            .get_context("webgl2")
+            .unwrap()
+            .unwrap()
+            .dyn_into::<WebGl2RenderingContext>()
+            .unwrap();
+        
+        // compile and attach the vertex and fragment shaders
+        let vertex_shader = compile_shader(
+            &ctx,
+            WebGl2RenderingContext::VERTEX_SHADER,
+            include_str!("identity.vert"),
+        );
+        let fragment_shader = compile_shader(
+            &ctx,
+            WebGl2RenderingContext::FRAGMENT_SHADER,
+            include_str!("inversive.frag"),
+        );
+        let program = ctx.create_program().unwrap();
+        ctx.attach_shader(&program, &vertex_shader);
+        ctx.attach_shader(&program, &fragment_shader);
+        ctx.link_program(&program);
+        let link_status = ctx
+            .get_program_parameter(&program, WebGl2RenderingContext::LINK_STATUS)
+            .as_bool()
+            .unwrap();
+        let link_msg = if link_status {
+            "Linked successfully"
+        } else {
+            "Linking failed"
+        };
+        console::log_1(&JsValue::from(link_msg));
+        ctx.use_program(Some(&program));
+        
+        /* DEBUG */
+        // print the maximum number of vectors that can be passed as
+        // uniforms to a fragment shader. the OpenGL ES 3.0 standard
+        // requires this maximum to be at least 224, as discussed in the
+        // documentation of the GL_MAX_FRAGMENT_UNIFORM_VECTORS parameter
+        // here:
+        //
+        //   https://registry.khronos.org/OpenGL-Refpages/es3.0/html/glGet.xhtml
+        //
+        // there are also other size limits. for example, on Aaron's
+        // machine, the the length of a float or genType array seems to be
+        // capped at 1024 elements
+        console::log_2(
+            &ctx.get_parameter(WebGl2RenderingContext::MAX_FRAGMENT_UNIFORM_VECTORS).unwrap(),
+            &JsValue::from("uniform vectors available")
+        );
+        
+        // find indices of vertex attributes and uniforms
+        let position_index = ctx.get_attrib_location(&program, "position") as u32;
+        let sphere_cnt_loc = ctx.get_uniform_location(&program, "sphere_cnt");
+        let sphere_sp_locs = get_uniform_array_locations::<SPHERE_MAX>(
+            &ctx, &program, "sphere_list", Some("sp")
+        );
+        let sphere_lt_locs = get_uniform_array_locations::<SPHERE_MAX>(
+            &ctx, &program, "sphere_list", Some("lt")
+        );
+        let color_locs = get_uniform_array_locations::<SPHERE_MAX>(
+            &ctx, &program, "color_list", None
+        );
+        let resolution_loc = ctx.get_uniform_location(&program, "resolution");
+        let shortdim_loc = ctx.get_uniform_location(&program, "shortdim");
+        let opacity_loc = ctx.get_uniform_location(&program, "opacity");
+        let highlight_loc = ctx.get_uniform_location(&program, "highlight");
+        let layer_threshold_loc = ctx.get_uniform_location(&program, "layer_threshold");
+        let debug_mode_loc = ctx.get_uniform_location(&program, "debug_mode");
+        
+        // create a vertex array and bind it to the graphics context
+        let vertex_array = ctx.create_vertex_array().unwrap();
+        ctx.bind_vertex_array(Some(&vertex_array));
+        
+        // set the vertex positions
+        const VERTEX_CNT: usize = 6;
+        let positions: [f32; 3*VERTEX_CNT] = [
+            // northwest triangle
+            -1.0, -1.0, 0.0,
+            -1.0,  1.0, 0.0,
+             1.0,  1.0, 0.0,
+            // southeast triangle
+            -1.0, -1.0, 0.0,
+             1.0,  1.0, 0.0,
+             1.0, -1.0, 0.0
+        ];
+        bind_vertex_attrib(&ctx, position_index, 3, &positions);
+        
+        // set up a repainting routine
+        let (_, start_animation_loop, _) = create_raf(move || {
+            // get the time step
+            let time = performance.now();
+            let time_step = 0.001*(time - last_time);
+            last_time = time;
+            
+            // get the navigation state
+            let pitch_up_val = pitch_up.get();
+            let pitch_down_val = pitch_down.get();
+            let yaw_right_val = yaw_right.get();
+            let yaw_left_val = yaw_left.get();
+            let roll_ccw_val = roll_ccw.get();
+            let roll_cw_val = roll_cw.get();
+            let zoom_in_val = zoom_in.get();
+            let zoom_out_val = zoom_out.get();
+            
+            // update the assembly's orientation
+            let ang_vel = {
+                let pitch = pitch_up_val - pitch_down_val;
+                let yaw = yaw_right_val - yaw_left_val;
+                let roll = roll_ccw_val - roll_cw_val;
+                if pitch != 0.0 || yaw != 0.0 || roll != 0.0 {
+                    ROT_SPEED * Vector3::new(-pitch, yaw, roll).normalize()
+                } else {
+                    Vector3::zeros()
+                }
+            };
+            let mut rotation_sp = rotation.fixed_view_mut::<3, 3>(0, 0);
+            rotation_sp.copy_from(
+                Rotation3::from_scaled_axis(time_step * ang_vel).matrix()
+            );
+            orientation = &rotation * &orientation;
+            
+            // update the assembly's location
+            let zoom = zoom_out_val - zoom_in_val;
+            location_z *= (time_step * ZOOM_SPEED * zoom).exp();
+            
+            if scene_changed.get() {
+                /* INSTRUMENTS */
+                // measure mean frame interval
+                frames_since_last_sample += 1;
+                if frames_since_last_sample >= SAMPLE_PERIOD {
+                    mean_frame_interval.set((time - last_sample_time) / (SAMPLE_PERIOD as f64));
+                    last_sample_time = time;
+                    frames_since_last_sample = 0;
+                }
+                
+                // find the map from construction space to world space
+                let location = {
+                    let u = -location_z;
+                    DMatrix::from_column_slice(5, 5, &[
+                        1.0, 0.0,   0.0, 0.0, 0.0,
+                        0.0, 1.0,   0.0, 0.0, 0.0,
+                        0.0, 0.0,   1.0, 0.0,   u,
+                        0.0, 0.0, 2.0*u, 1.0, u*u,
+                        0.0, 0.0,   0.0, 0.0, 1.0
+                    ])
+                };
+                let construction_to_world = &location * &orientation;
+                
+                // update the construction
+                sphere_vec.clear();
+                sphere_vec.push(&construction_to_world * DVector::<f64>::from_column_slice(&[0.5, 0.5, 0.0, 0.5, -0.25]));
+                sphere_vec.push(&construction_to_world * DVector::<f64>::from_column_slice(&[-0.5, -0.5, 0.0, 0.5, -0.25]));
+                sphere_vec.push(&construction_to_world * DVector::<f64>::from_column_slice(&[0.0, 0.0, 0.0, 0.4, -0.625]));
+                color_vec.clear();
+                color_vec.push([1.00_f32, 0.25_f32, 0.00_f32]);
+                color_vec.push([0.00_f32, 0.25_f32, 1.00_f32]);
+                color_vec.push([0.75_f32, 0.75_f32, 0.75_f32]);
+                
+                // set the resolution
+                let width = canvas.width() as f32;
+                let height = canvas.height() as f32;
+                ctx.uniform2f(resolution_loc.as_ref(), width, height);
+                ctx.uniform1f(shortdim_loc.as_ref(), width.min(height));
+                
+                // pass the construction
+                ctx.uniform1i(sphere_cnt_loc.as_ref(), sphere_vec.len() as i32);
+                for n in 0..sphere_vec.len() {
+                    let v = &sphere_vec[n];
+                    ctx.uniform3f(
+                        sphere_sp_locs[n].as_ref(),
+                        v[0] as f32, v[1] as f32, v[2] as f32
+                    );
+                    ctx.uniform2f(
+                        sphere_lt_locs[n].as_ref(),
+                        v[3] as f32, v[4] as f32
+                    );
+                    ctx.uniform3fv_with_f32_array(
+                        color_locs[n].as_ref(),
+                        &color_vec[n]
+                    );
+                }
+                
+                // pass the display parameters
+                ctx.uniform1f(opacity_loc.as_ref(), OPACITY);
+                ctx.uniform1f(highlight_loc.as_ref(), HIGHLIGHT);
+                ctx.uniform1i(layer_threshold_loc.as_ref(), LAYER_THRESHOLD);
+                ctx.uniform1i(debug_mode_loc.as_ref(), DEBUG_MODE);
+                
+                // draw the scene
+                ctx.draw_arrays(WebGl2RenderingContext::TRIANGLES, 0, VERTEX_CNT as i32);
+                
+                // clear the scene change flag
+                scene_changed.set(false);
+            } else {
+                frames_since_last_sample = 0;
+                mean_frame_interval.set(-1.0);
+            }
+        });
+        start_animation_loop();
+    });
+    
     view! {
-        /* [TO DO] switch back to integer-valued parameters when that becomes
+        /* TO DO */
-        possible again */
+        // switch back to integer-valued parameters when that becomes possible
-        canvas(width="750", height="750", tabindex="0")
+        // again
+        canvas(ref=display, width="750", height="750", tabindex="0")
     }
 }

app-proto/sketch-outline/src/identity.vert

@@ -0,0 +1,7 @@
+#version 300 es
+
+in vec4 position;
+
+void main() {
+    gl_Position = position;
+}

app-proto/sketch-outline/src/inversive.frag

@@ -0,0 +1,227 @@
+#version 300 es
+
+precision highp float;
+
+out vec4 outColor;
+
+// --- inversive geometry ---
+
+struct vecInv {
+    vec3 sp;
+    vec2 lt;
+};
+
+// --- uniforms ---
+
+// construction. the SPHERE_MAX array size seems to affect frame rate a lot,
+// even though we should only be using the first few elements of each array
+const int SPHERE_MAX = 200;
+uniform int sphere_cnt;
+uniform vecInv sphere_list[SPHERE_MAX];
+uniform vec3 color_list[SPHERE_MAX];
+
+// view
+uniform vec2 resolution;
+uniform float shortdim;
+
+// controls
+uniform float opacity;
+uniform float highlight;
+uniform int layer_threshold;
+uniform bool debug_mode;
+
+// light and camera
+const float focal_slope = 0.3;
+const vec3 light_dir = normalize(vec3(2., 2., 1.));
+const float ixn_threshold = 0.005;
+const float INTERIOR_DIMMING = 0.7;
+
+// --- sRGB ---
+
+// map colors from RGB space to sRGB space, as specified in the sRGB standard
+// (IEC 61966-2-1:1999)
+//
+//   https://www.color.org/sRGB.pdf
+//   https://www.color.org/chardata/rgb/srgb.xalter
+//
+// in RGB space, color value is proportional to light intensity, so linear
+// color-vector interpolation corresponds to physical light mixing. in sRGB
+// space, the color encoding used by many monitors, we use more of the value
+// interval to represent low intensities, and less of the interval to represent
+// high intensities. this improves color quantization
+
+float sRGB(float t) {
+    if (t <= 0.0031308) {
+        return 12.92*t;
+    } else {
+        return 1.055*pow(t, 5./12.) - 0.055;
+    }
+}
+
+vec3 sRGB(vec3 color) {
+    return vec3(sRGB(color.r), sRGB(color.g), sRGB(color.b));
+}
+
+// --- shading ---
+
+struct taggedFrag {
+    int id;
+    vec4 color;
+    vec3 pt;
+    vec3 normal;
+};
+
+taggedFrag[2] sort(taggedFrag a, taggedFrag b) {
+    taggedFrag[2] result;
+    if (a.pt.z > b.pt.z) {
+        result[0] = a;
+        result[1] = b;
+    } else {
+        result[0] = b;
+        result[1] = a;
+    }
+    return result;
+}
+
+taggedFrag sphere_shading(vecInv v, vec3 pt, vec3 base_color, int id) {
+    // the expression for normal needs to be checked. it's supposed to give the
+    // negative gradient of the lorentz product between the impact point vector
+    // and the sphere vector with respect to the coordinates of the impact
+    // point. i calculated it in my head and decided that the result looked good
+    // enough for now
+    vec3 normal = normalize(-v.sp + 2.*v.lt.s*pt);
+    
+    float incidence = dot(normal, light_dir);
+    float illum = mix(0.4, 1.0, max(incidence, 0.0));
+    return taggedFrag(id, vec4(illum * base_color, opacity), pt, normal);
+}
+
+// --- ray-casting ---
+
+// if `a/b` is less than this threshold, we approximate `a*u^2 + b*u + c` by
+// the linear function `b*u + c`
+const float DEG_THRESHOLD = 1e-9;
+
+// the depths, represented as multiples of `dir`, where the line generated by
+// `dir` hits the sphere represented by `v`. if both depths are positive, the
+// smaller one is returned in the first component. if only one depth is
+// positive, it could be returned in either component
+vec2 sphere_cast(vecInv v, vec3 dir) {
+    float a = -v.lt.s * dot(dir, dir);
+    float b = dot(v.sp, dir);
+    float c = -v.lt.t;
+    
+    float adjust = 4.*a*c/(b*b);
+    if (adjust < 1.) {
+        // as long as `b` is non-zero, the linear approximation of
+        //
+        //   a*u^2 + b*u + c
+        //
+        // at `u = 0` will reach zero at a finite depth `u_lin`. the root of the
+        // quadratic adjacent to `u_lin` is stored in `lin_root`. if both roots
+        // have the same sign, `lin_root` will be the one closer to `u = 0`
+        float square_rect_ratio = 1. + sqrt(1. - adjust);
+        float lin_root = -(2.*c)/b / square_rect_ratio;
+        if (abs(a) > DEG_THRESHOLD * abs(b)) {
+            return vec2(lin_root, -b/(2.*a) * square_rect_ratio);
+        } else {
+            return vec2(lin_root, -1.);
+        }
+    } else {
+        // the line through `dir` misses the sphere completely
+        return vec2(-1., -1.);
+    }
+}
+
+void main() {
+    vec2 scr = (2.*gl_FragCoord.xy - resolution) / shortdim;
+    vec3 dir = vec3(focal_slope * scr, -1.);
+    
+    // cast rays through the spheres
+    const int LAYER_MAX = 12;
+    taggedFrag frags [LAYER_MAX];
+    int layer_cnt = 0;
+    for (int id = 0; id < sphere_cnt; ++id) {
+        // find out where the ray hits the sphere
+        vec2 hit_depths = sphere_cast(sphere_list[id], dir);
+        
+        // insertion-sort the fragments we hit into the fragment list
+        float dimming = 1.;
+        for (int side = 0; side < 2; ++side) {
+            float hit_z = -hit_depths[side];
+            if (0. > hit_z) {
+                for (int layer = layer_cnt; layer >= 0; --layer) {
+                    if (layer < 1 || frags[layer-1].pt.z >= hit_z) {
+                        // we're not as close to the screen as the fragment
+                        // before the empty slot, so insert here
+                        if (layer < LAYER_MAX) {
+                            frags[layer] = sphere_shading(
+                                sphere_list[id],
+                                hit_depths[side] * dir,
+                                dimming * color_list[id],
+                                id
+                            );
+                        }
+                        break;
+                    } else {
+                        // we're closer to the screen than the fragment before
+                        // the empty slot, so move that fragment into the empty
+                        // slot
+                        frags[layer] = frags[layer-1];
+                    }
+                }
+                layer_cnt = min(layer_cnt + 1, LAYER_MAX);
+                dimming = INTERIOR_DIMMING;
+            }
+        }
+    }
+    
+    /* DEBUG */
+    // in debug mode, show the layer count instead of the shaded image
+    if (debug_mode) {
+        // at the bottom of the screen, show the color scale instead of the
+        // layer count
+        if (gl_FragCoord.y < 10.) layer_cnt = int(16. * gl_FragCoord.x / resolution.x);
+        
+        // convert number to color
+        ivec3 bits = layer_cnt / ivec3(1, 2, 4);
+        vec3 color = mod(vec3(bits), 2.);
+        if (layer_cnt % 16 >= 8) {
+            color = mix(color, vec3(0.5), 0.5);
+        }
+        outColor = vec4(color, 1.);
+        return;
+    }
+    
+    // highlight intersections and cusps
+    for (int i = layer_cnt-1; i >= 1; --i) {
+        // intersections
+        taggedFrag frag0 = frags[i];
+        taggedFrag frag1 = frags[i-1];
+        float ixn_sin = length(cross(frag0.normal, frag1.normal));
+        vec3 disp = frag0.pt - frag1.pt;
+        float ixn_dist = max(
+            abs(dot(frag1.normal, disp)),
+            abs(dot(frag0.normal, disp))
+        ) / ixn_sin;
+        float ixn_highlight = 0.5 * highlight * (1. - smoothstep(2./3.*ixn_threshold, 1.5*ixn_threshold, ixn_dist));
+        frags[i].color = mix(frags[i].color, vec4(1.), ixn_highlight);
+        frags[i-1].color = mix(frags[i-1].color, vec4(1.), ixn_highlight);
+        
+        // cusps
+        float cusp_cos = abs(dot(dir, frag0.normal));
+        float cusp_threshold = 2.*sqrt(ixn_threshold * sphere_list[frag0.id].lt.s);
+        float cusp_highlight = highlight * (1. - smoothstep(2./3.*cusp_threshold, 1.5*cusp_threshold, cusp_cos));
+        frags[i].color = mix(frags[i].color, vec4(1.), cusp_highlight);
+    }
+    
+    // composite the sphere fragments
+    vec3 color = vec3(0.);
+    for (int i = layer_cnt-1; i >= layer_threshold; --i) {
+        if (frags[i].pt.z < 0.) {
+            vec4 frag_color = frags[i].color;
+            color = mix(color, frag_color.rgb, frag_color.a);
+        }
+    }
+    outColor = vec4(sRGB(color), 1.);
+}

app-proto/sketch-outline/src/main.rs

@@ -29,14 +29,14 @@ fn main() {
                         Element {
                             id: String::from("wing_b"),
                             label: String::from("Wing B"),
-                            color: [1.00_f32, 0.25_f32, 0.00_f32],
+                            color: [0.00_f32, 0.25_f32, 1.00_f32],
                             rep: DVector::<f64>::from_column_slice(&[-0.5, -0.5, 0.0, 0.5, -0.25])
                         },
                         Element {
                             id: String::from("central"),
                             label: String::from("Central"),
                             color: [0.75_f32, 0.75_f32, 0.75_f32],
-                            rep: DVector::<f64>::from_column_slice(&[0.0, 0.0, 0.0, 0.25, -1.0])
+                            rep: DVector::<f64>::from_column_slice(&[0.0, 0.0, 0.0, 0.25, 1.0])
                         }
                     ])
                 }